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On the uniqueness of convex-ranged probabilities

Amarante, Massimiliano

We provide an alternative proof of a theorem of Marinacci [2] regarding the equality of two convex-ranged measures. Specifically, we show that, if P and Q are two nonatomic, countably additive probabilities on a measurable space (S, Σ), the condition [∃A∗ ∈ Σ with 0 < P(A∗) < 1 such that P(A∗) = P(B)=⇒ Q(A∗) = Q(B) whenever B∈Σ] is equivalent to the condition [∀A,B ∈ Σ P(A) > P(B)=⇒ Q(A) ≥ Q(B)]. Moreover, either one is equivalent to P = Q.

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Academic Units
Economics
Publisher
Department of Economics, Columbia University
Series
Department of Economics Discussion Papers, 0203-24
Published Here
March 24, 2011

Notes

August 2003

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